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Belief Uncertainty in Software Models


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This presentation discusses the representation of Belief Uncertainty in software models. This kind of uncertainty refers to the situation in which the modeler, or any other belief agent, is uncertain about the behavior of the system, or the statements that the model expresses about it. In this work, we propose to assign a degree of belief to model statements (let they be constraints, or any other model expression), which is expressed by a probability (called credence, in statistical terms) that represents a quantification of such a subjective degree of belief. We discuss how it can be represented using current modeling notations, and how to operate with it in order to make informed decisions.

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Belief Uncertainty in Software Models

  1. 1. Belief Uncertainty in Software Models MISE 2019 Montreal, Canada, May 26-27, 2019 Loli Burgueño1,2, Robert Clarisó1, Jordi Cabot3, Sébastien Gérard2 and Antonio Vallecillo4 1Open University of Catalonia, 2CEA-LIST, 3ICREA, 4University of Málaga
  2. 2. A simple example of a hotel room 2 Temp. sensor Smoke detector Alarm center CO detector
  3. 3. A simple example of a hotel room 3
  4. 4. System attributes, operations, and constraints 4 class AlarmCenter attributes hightTemp : UBoolean derive: > 30.0 hightCOLevel : UBoolean derive: > 20 smoke : UBoolean derive: fireAlert : UBoolean derive: self.highTemp and self.highCOLevel and self.smoke operations isHot() : UBoolean = self.tempSensor.temperature > 25 isCold() : UBoolean = self.tempSensor.temperature < 18 constraints inv TempPrecision: self.temperature.uncertainty() <= 0.2 [Bertoa et al “Expressing Measurement Uncertainty in OCL/UML Datatypes. ECMFA 2018: 46-62]
  5. 5. Some Belief Statements about the (model of the) system  The CO and smoke detectors that we bought have a reliability of 90% (i.e., 10% of their readings are not meaningful)  We can only be 98% sure that the precision of the Temperature sensor is 0.5o, as indicated in its datasheet  We are 95% confident that the presence of high temperature, high CO level and smoke really means that there is a fire in the room  Bob is from the south, so he only assigns a credibility of 50% to the operations that indicate if the room is hot or cold. In contrast, Mary thinks they are 99% accurate  Room #3 is close to the kitchen and frequently emits alarms. Everybody thinks that 90% of them are false positives  Joe the modeler doubts that the type of attribute “number” of class “Room” is Integer. He thinks it may contain characters different from digits.  Lucy the modeler is unsure if an “AlarmCenter” has to be attached to only one single Room. She thinks they can also be attached to several. 5 [About the credibility of the values] [From individual belief agents] [About individual instances] [About the model itself: relations] [About the behavioral rules] [About the uncertainty of the values] [About the model itself: types] >> How to represent these uncertainties in the system specifications? >> How to incorporate them into the system structural and behavioral models?
  6. 6. The characters (in order of appearance…)  Uncertainty  The quality or state the involves imperfect or unknown information  It can be aleatory (variations in measurement) or epistemic (lack of knowledge)  Belief uncertainty  A kind of epistemic uncertainty in which the modeler, or any other belief agent, is uncertain about any of the statements made about the system or its environment. By nature, it is always subjective.  Belief agent  An entity (human, institution, even a machine) that holds one or more beliefs  Belief statement  Statement qualified by a degree of belief  Degree of belief  Confidence assigned to a statement by a belief agent. Normally expressed by quantitative or qualitative methods (e.g., a grade or a probability) 6
  7. 7. Current approaches to represent and operate with Belief Uncertainty 7
  8. 8. Our contribution  A mechanism able to assign a degree of belief to model statements  A method to operate with the degrees of beliefs and automatically propagate them through the system operations How do we do that?  Explicit representation of Belief Agents (including a default one)  Degrees of belief represented by means of Bayesian probabilities (Credence)  Bayesian probability is the most classical model for expressing and operating with subjective information, and hence for quantifying beliefs  Credence is a statistical term that refers to a measure of belief strength, which expresses how much an agent believes that a proposition is true  Credence values can be based entirely on subjective feelings  Credence is better understood in the context of gambling, where this concept is directly related to the odds at which a rational person would place a bet  UML Profile + operational semantics 8
  9. 9. UML Profile 9
  10. 10. Operationalization  A list of pairs (BeliefAgent,credence) for every model statement subject to Belief Uncertainty  Operations to add and remove pairs from the list of pairs  Query operation to know the credence of a statement 10 isHot_Beliefs : Set(Tuple(beliefAgent : BeliefAgent, degreeOfBelief : Real)) isHot_BeliefsAdd(ba : BeliefAgent, d : Real) post: self.isHot_Beliefs = self.isHot_Beliefs@pre->reject(t|t.beliefAgent=ba)-> including(Tuple{beliefAgent:ba,degreeOfBelief:d}) isHot_credence(a:BeliefAgent): Real = let baBoD : … = self.isHot_Beliefs->select(t|t.beliefAgent = a) in let baBoDnull : … = self.isHot_Beliefs->select(t|t.beliefAgent = null) in if baBoD->isEmpty then -- no explicit credence by “a” if baBoDnull->notEmpty then -- but if default value exists baBoDnull->collect(degreeOfBelief)->any(true) else 1.0 endif else baBoD->collect(degreeOfBelief)->any(true) endif
  11. 11. Running the system… 11 Hotel> !new BeliefAgent('Bob') Hotel> !new BeliefAgent('Mary') Hotel> !r1.isHot_BeliefsAdd(Bob,0.5) Hotel> !r1.isHot_BeliefsAdd(Mary,0.99) Hotel> !r1.isHot_BeliefsAdd(null,0.95) Hotel> Hotel> ?r1.isHot() -> UBoolean(true,1.0) : Uboolean Hotel> ?r1.isHot_credence(Bob) -> 0.5 : Real Hotel> ?r1.isHot_credence(Mary) -> 0.99 : Real Hotel> ?r1.isHot_credence(null) -> 0.95 : Real
  12. 12. Credence propagation on dependent belief statements 12 fireAlert_credence(ba:BeliefAgent): Real = let baBoD : Set(Tuple(beliefAgent:BeliefAgent, degreeOfBelief:Real)) = self.fireAlert_Beliefs->select(t|t.beliefAgent = ba) in (if baBoD->isEmpty then … else baBoD->collect(degreeOfBelief)->any(true) endif) * self.fireAlertDeriveExpr_credence(ba) fireAlertDeriveExpr_credence(ba:BeliefAgent): Real = let baBoD : Set(Tuple(beliefAgent:BeliefAgent, degreeOfBelief:Real)) = self.fireAlertDeriveExpr_Beliefs->select(t|t.beliefAgent = ba) in (if baBoD->isEmpty then … else baBoD->collect(degreeOfBelief)->any(true) endif) * highTemp_credence(ba) * highCOLevel_credence(ba) * smoke_credence(ba)
  13. 13. Running the system… 13 Hotel> !r2.alarmCenter. fireAlert_BeliefsAdd(null,0.1) Hotel> !r1.alarmCenter.fireAlert_BeliefsAdd(Bob,0.99) Hotel> !r1.alarmCenter.fireAlertDeriveExpr_BeliefsAdd(Bob,0.95) Hotel> !r1.alarmCenter.highTemp_BeliefsAdd(Bob,0.99) Hotel> !r1.alarmCenter.highCOLevel_BeliefsAdd(Bob,0.99) Hotel> !r1.alarmCenter.smoke_BeliefsAdd(Bob,0.99) Hotel> Hotel> ?r1.alarmCenter.fireAlert -> UBoolean(true,0.99) : UBoolean Hotel> ?r1.alarmCenter.fireAlert_credence(Bob) -> 0.9125662095 : Real Hotel> ?r1.alarmCenter.fireAlert_credence(Mary) -> 1.0 : Real Hotel> ?r1.alarmCenter.fireAlert_credence(null) -> 1.0 : Real Hotel> Hotel> ?r2.alarmCenter.fireAlert_credence(Bob) -> 0.04562831047 : Real
  14. 14. Conclusions and future work  Explicit representation and management of belief uncertainty in software models…  …in terms of degrees of belief assigned to the model statements by separate belief agents…  …about the credibility of  The values of the represented (physical) elements  The measurement uncertainty of these values  The expressions that model the behavior of the system  The way in which we have modeled the system (types of the attributes, types of relationships and their cardinalities, etc.)  Future work  Associating evidences to belief statements  Representing degrees of beliefs in other types of models (use cases, sequence diagrams, pre- and postconditions, …)  Industrial case studies and further application domains (e.g., model inference, model mining)  Empirical validation with industrial modelers 14
  15. 15. Further claims (1/2)  Claim 1: Our current software models are not fully capable of faithfully representing all key relevant aspects of physical systems. These systems are never crisp, they are subject to different kinds of uncertainties. This our models should be able to reflect. 15 (
  16. 16. Further claims (2/2)  Claim 2: Modeling notations and tools (e.g. DSLs) are of little value without well defined methods and processes, which in turn require solid principles. We should always ask ourselves if our modeling notations take into account the principles that govern our physical systems, or are they mere shallow and cosmetic descriptions of them? 16 “The man who grasps principles can successfully handle his own methods. The man who tries methods, ignoring principles, is sure to have trouble” Ralph Waldo Emerson
  17. 17. Belief Uncertainty in Software Models MISE 2019 Montreal, Canada, May 26-27, 2019 Loli Burgueño1,2, Robert Clarisó1, Jordi Cabot3, Sébastien Gérard2 and Antonio Vallecillo4 1Open University of Catalonia, 2CEA-LIST, 3ICREA, 4Málaga University